Measuring by eye

In this activity, you will be given two strips of paper printed with:

  1. An empty rectangular box
  2. A ruler

Follow these steps

  1. Without using the ruler at all, subdivide by eye the rectangular box into three equal-sized sections, like this:

  1. Now the ruler comes into play. Measure the lengths of your three subdivisions using the ruler.

  2. Record your three measurements in this spreadsheet. Also create an ID for yourself, for example your initials or the initials of your favorite aunt, baseball player, or whatever.

Link to a spreadsheet for data entry

  1. Once everyone has entered their measurements, copy the following statement into the console in Posit.cloud and run it to create a data frame named Thirds.
Thirds <- readr::read_csv("https://docs.google.com/spreadsheets/d/e/2PACX-1vT_asFV5LD312bYaGgHK3F91kgLVSiaQpNhggDilfPKAiDBNz9iueOiYWKgAtRRwkFlOz6U9znbiMGK/pub?gid=0&single=true&output=csv")
  1. Follow the instructions given in class. These will have you

    1. Calculate the variance of the three measurements for each student separately. Use mutate() to calculate modulus <- ((left-middle)^2 + (left-right)^2 + (middle-right)^2)/3, storing the result back in Thirds as a variable named modulus.

    2. Analyze how good you and your colleagues are at sub-dividing evenly by eye.

    3. Create a new dataframe that is Thirds re-arranged into “long” format.

     Long_form <- tidyr::pivot_longer(Thirds, !Student_initials, names_to = "position")
    1. Group Long_form by student initials and calculate the variance of value. Compare these values to those stored under modulus in Thirds.

Questions

  1. Why is it not useful, for the purposes of measuring the quality of the subdivision, to calculate the mean of the left, middle, and right segment lengths?

  2. What did you look for in Step (ii)?